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Canadian Conference on Computational Chemistry Halifax, July 19 - 24, 2009. Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics. Prof. H. Bernhard Schlegel Department of Chemistry Wayne State University Current Research Group Dr. Peng Tao Dr. Barbara Munk - PowerPoint PPT Presentation
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Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics
Prof. H. Bernhard SchlegelDepartment of ChemistryWayne State University
Current Research GroupDr. Peng Tao Dr. Barbara MunkJia Zhou Jason SonkBrian Psciuk Adam Birkholz
Recent Group MembersProf. Xiaosong Li Dr. Hrant Hratchian Prof. Jason Sonnenberg Dr. Stan SmithProf. Smriti Anand Dr. Jie (Jessy) LiDr. John Knox Michael Cato
Canadian Conference on Computational Chemistry
Halifax, July 19 - 24, 2009
Overview
AIMD study of non-statistical behavior acetone radical cation and 2,4-pentanedione radical cation dissociation
AIMD study of a Coulomb explosion: dissociation of CH2=NHn+, (n=0,1,2,3)
Electronic response of molecules in short, intense laser pulses
Applications of Ab Initio Molecular Dynamics
Jia Zhou
ChemistryWayne State U.
Prof. Smriti Anand
Northern VirginiaCommunity College
Dr. Jie Li
Genome CenterUC Davis
Ab Initio Molecular Dynamics (AIMD)
AIMD – electronic structure calculations combined with classical trajectory calculations
Every time the forces on the atoms in a molecule are needed, do an electronic structure calculation
Born – Oppenheimer (BO) method: converge the wavefunction at each step in the trajectory
Extended Lagrangian methods: propagate the wavefunction along with the geometry
Car-Parrinello – plane-wave basis, propagate MO’s
ADMP – atom centered basis, propagate density matrix
Ab Initio Classical Trajectory on theBorn-Oppenheimer Surface Using Hessians
Calculate the energy,gradient and Hessian
Solve the classicalequations of motion on a
local 5th order polynomial surface
Millam, J. M.; Bakken, V.; Chen, W.; Hase, W. L.; Schlegel, H. B.; J. Chem. Phys. 1999, 111, 3800-5.
Dissociation of Acetone Radical Cation
Dissociation of C3H6O+• has been of interest for many years now The enol ion is produced via the McLafferty rearrangement.
The enol form isomerizes to the keto form, activating the newly formed methyl group, and dissociates to form an acetyl cation and methyl radical
Dissociation behaves in a non-statistical manner favoring the loss of newly formed methyl group by 1.1-1.7 to 1
H3C CH3
O
CH3CO + CH3H3C CH2
OH
*
O CH2R H transfer O CHRH
OH CHR+ _
H2C CHR
H3C CH2
OH+
Energy Dependence of the Branching Ratio
Osterheld, T. H.; Brauman, J. I.; J. Am. Chem. Soc. 1993, 115, 10311-10316.
Potential Energy Profile (CBS-APNO)
-25
-15
-5
5
15
25
35
45
Re
lati
ve
En
erg
y (
kc
al/
mo
l)
Ketene/Methane complex
TS for Methane Elimination
CH3CO+/ CH3
• complex
Anand, S.; Schlegel, H. B. Phys. Chem. Chem. Phys. 2004, 6, 5166.
Improved Potential Energy Surfaces using Bond Additivity Corrections (BAC)
The most important corrections needed for acetone radical cation dissociation reaction are for C-C bond stretching potentials.
BAC (bond additivity correction) add simple corrections to get better energetics for the reaction E = E′+ ∆E ∆E = AC-C Exp{-αC-C RC-C1} + AC-C Exp{- αC-C RC-C2} add the corresponding corrections to gradient and hessian
G = G′+ ∂(∆E)/∂x H = H′+ ∂2(∆E)/∂x2
A and α are parameters obtained by fitting to high level energies
Initial Energy
(kcal/mol)
Branching Ratio
Average Etranslation
(kcal/mol)
Average Dissociation
Time (fs)
1
2
1.43
1.88
2.7 / 2.0
3.3 / 2.7
181 / 224
177 / 240
10 1.70 4.2 / 2.3 147 / 186
18 1.50 4.2 / 2.8 140 / 167
Branching Ratios for Microcanonical Ensemble
Energy assigned 3rd mode 6th mode 8th mode
0 1.10:1
1 kcal/mol 1.59:1 1.58:1 1.54:1
2 kcal/mol 1.84:1 2.31:1 1.82:1
4 kcal/mol 1.46:1 1.85:1 2.36:1
8 kcal/mol 1.55:1 2.03:1 2.76:1
* plus 0.5 kcal/mol in transition vector
Effect of Adding Energy to Specific Vibrational Modes
Dissociation of Chemically Activated Pentane-2,4-dione Radical Cation
H3C CH2 (CH2)3R
O O
H3C CH2 CH2
O HO
H3Ca CbH2 CcH3
O O
- e
*
chemically activated intermediate
- RCH=CH2
CaH3C(O)CbH2CO+ + .CcH3
CaH3C(O)CbH2. + CcH3CO+
CaH3CO+ + .CbH2C(O)CcH3
.CaH3 + +OCCbH2C(O)CcH3
The enol radical cation can be produced via the McLafferty rearrangement
Energy is localized in terminal C-C bond, but can flow to the other C-C bonds
Zhou, J.; Schlegel, H. B.; J. Phys. Chem. A 2009, 113, 1453
Potential Energy Surface for Pentanedione Radical Cation
H3C CH2 CH3
O O
29%
45%2.3%
0%
*
Kinetic Scheme for Pentanedione Radical Cation
H3C CH2 CH3
O O
H3C CH2 CH3
O O
H3C CH2 CH3
O O
H3C CH2 CH3
O O
H3C CH2 CH3
O O
*H3C CH2 CH3
O O
*H3C CH2 CH3
O O
*H3C CH2 CH3
O O
*k4 k3'
k1k2
proton transfer andester-like product
k6k6
loss ofactive methyl
loss ofactive acetyl
loss ofspectator methyl
loss ofspectator acetyl
initial activation of the terminal
CC bond
enol
k5
k1k1fast
k3fast
k3
k2k2fast
indicates activated bond*
k1fast = 0.018 fs-1
k2fast = 0.040 fs-1
k3fast = 0.018 fs-1
k1 = 0.00114 fs-1, k2 = 0.012 fs-1
k3=k3' = 0.0032 fs-1, k4 = 0.001 fs-1
k5 = 0.00167 fs-1, k6 = 0.002 fs-1
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 00
2 0
4 0
6 0
8 0
1 0 0
T im e fs
A c tiv e M e th y l
A c tiv e A c e ty l
S p e c ta to r A c e ty l
Time (fs)
Dissociation of Methanimine and its Cations, CH2=NHn+ (n=0,1,2,3)
Simplest example of a molecule with a CN double bond, also known as methyleneimine and formaldimine
As electrons are removed, bonding should become weaker, finally leading to a Coulomb explosion
CH2NH formed by pyrolysis of amines and azides, and seen in interstellar clouds
Monocation also well studied experimentally, but little or no experimental information on higher cations
Many theoretical studies over the years, but at many different levels of theory
Structures and energetics calculated by CBS-APNO Ab initio molecular dynamics by B3LYP/6-311G(d,p)
Dissociation of H2CNH
Dissociation of H2CNH+
Dissociation of H2NCH2+
Dissociation of H2NCH3+
Direct vs Indirect Dissociation of H2CNH
Direct (no hydrogen rearrangement before dissociation)
Indirect (hydrogen migration before dissociation)
Ab Initio Molecular Dynamicsof CH2=NHn+ Dissociation
Neutral H2CNH (200 kcal/mol initial energy) CH dissociation (28% direct, 4% indirect) NH dissociation (13% direct, 3% indirect) Triple dissociation (22% HCN+H+H, 9% HNC+H+H) Molecular dissociation (9 % HCN+H2, 10% HNC+H2)
Monocation H2CNH+ (150 kcal/mol initial energy) HCNH+ + H (68% direct, 13% indirect) H2CN+ + H HCNH+ + H (10%) Molecular dissociation (3 % HCN++H2, 3% HNC++H2)
Dication H2NCH2+ (120 kcal/mol initial energy) HCNH+ + H+ (51% direct, 24% indirect) H2NC+ + H+ (10%) No reaction (13%)
Time Dependent Simulations of Molecules in Strong Fields
Prof. Xiaosong LiUniversity of Washington
Dr. Stan Smith, Temple U.
Prof. Robert Levis, Temple U.
Jason Sonk, WSU
Electronic Response of Molecules Short, Intense Laser Pulses
For intensities of 1014 W/cm2, the electric field of the laser pulse is comparable to Coulombic attraction felt by the valence electrons – strong field chemistry
Need to simulate the response of the electrons to short, intense pulses
Time dependent Schrodinger equations in terms of ground and excited states
= Ci(t) i i ħ dCi(t)/dt = Hij(t) Ci(t) Requires the energies of the field free states and the transition dipoles between them Need to limit the expansion to a subset of the excitations – TD-CIS, TD-CISD
Time dependent Hartree-Fock equations in terms of the density matrix
i ħ dP(t)/dt = [F(t), P(t)]
For constant F, can use a unitary transformation to integrate analyticallyP(ti+1) = V P(ti) V† V = exp{ i t F }
Fock matrix is time dependent because of the applied field and because of the time dependence of the density (requires small integration step size – 0.05 au)
Hydrogen Moleculeaug-cc-pVTZ basis plus 3 sets of diffuse sp shells
Emax = 0.07 au (1.7 1014 W/cm2), = 0.06 au (760 nm)(a)
(b)
(c)
(b)
(c)
(d)
(e)
(f)
TD-CIS TD-CISD TD-HFInstantaneous dipole response
Fourier transform of the residual dipole response
Energy (au)
Time (0.05×au)
Butadiene
1.75
1.80
1.85
1.90
1.95
2.00
0.00
0.05
0.10
0.15
0.20
0.25
1.982
1.984
1.986
1.988
1.990
1.992
1.994
1.996
1.998
2.000
2.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
-2 0 2 4 6 8 10 12 14 16 18
1.988
1.990
1.992
1.994
1.996
1.998
2.000
-2 0 2 4 6 8 10 12 14 16 18
0.000
0.002
0.004
0.006
0.008
0.010
HOMO HOMO-1
LUMO LUMO+1
n(a
u)
HOMO-2 HOMO-3
n(a
u)
LUMO+2 LUMO+3
Time (fs)
HOMO-4 HOMO-5
Time (fs)
LUMO+4 LUMO+5
-2 0 2 4 6 8 10 12 14 16 18-0.6-0.4-0.20.00.20.40.6-4
-2
0
2
4-0.06-0.04-0.020.000.020.040.06
q(a
u)
Time (fs)
C1
C2
C3
C4
d(a
u) d
x
dy
(au
)8.75×1013 W/cm2
760 nm
HF/6-31G(d,p)
t = 0.0012 fs
H
H
H
H
H
H
Laser pulse
Dipole
Charges
Populations ofoccupied orbitals
Populations ofunoccupied orbitals
Butadiene, Hexatriene and NaphthaleneTD-CIS/6-31G(d,p), = 0.06 au (760 nm)
Excited state weights in the final wavefunction
RPACISCIS(D)CISDEOM-CCSD
Excited State Energies of Butadiene
* Transition Dipoles for Butadiene (6-31G(d,p) basis)
Response of 2 and 3 Level Systemsto a 3 Cycle Gaussian Pulse
2 4 6 8fs
0.04
0.02
0.02
0.04
I
0.00
0.25
0.00
0.25
0.35
Response of the States of Butadieneto a 3 Cycle Gaussian Pulse
TD-CIS 1Ag (gs) 1Bu 1Ag 1Bu
TD-EOMCC
TD-CIS response vs number of states
A large number of states are needed for the response to be stable
Lowest states are well separated
Higher states form a quasi-continuum
Most of the higher lying states are needed primarily to represent the polarization of the molecule in the field
20 40 60 80 100
0 .2
0 .4
0 .6
0 .8
1 .0
State Number
80 100 120 140 160Number of States
0.01
0.02
0.03
noitcnufevaW
tneiciffeoC
TD-CIS in a Reduced Space
Perturbation theory for the effective polarizability of the low lying states
Finite difference method for the effective polarizability
where D' is the matrix of transition dipoles with the elements between the low lying states set to zero
Integrate TD-CI equations with polarizability
22 | | /( )
high lying
i k ik
i k r
2( ( ) 2 (0) ( )) / ( ) ( ' )Ti i i i i e e e e U H D e U
1
2( ) ( ) ( ) ( ) ( ) ( ) ( )
i ij j ij i ij ij ijii dC t dt H t C t H t t t t e e eD
2 4 6 8 1 0 1 2 1 4 1 6
3
2
1
1
2
3
2 4 6 8 1 0 1 2 1 4 1 6
3
2
1
1
2
3
0 .0 0 .2 0 .4 0 .6 0 .8 1 .00 .000
0 .005
0 .010
0 .015
0 .020
0 .025
TD-CIS in a Reduced SpaceButadiene, TD-CIS/6-31G(d,p)
Emax = 0.05 au (8.75 1013 W/cm2), = 0.06 au (760 nm)
Large CIS space Small CIS space with polarizability
0 .0 0 .2 0 .4 0 .6 0 .8 1 .00 .0 00
0 .0 05
0 .0 10
0 .0 15
0 .0 20
0 .0 25
Instantaneous DipoleInstantaneous Dipole
Wavefunction Coefficients
Wavefunction Coefficients
Time (fs)
Energy (au)
Time (fs)
Energy (au)
Response of Butadieneto a 3 Cycle Gaussian Pulse(=0.6 au, 6-31G(d,p) basis)
RPA
TD-CIS(D)
TD-CIS
TD-EOMCC
Transition Dipoles for Butadiene(CIS)
Response of Butadieneto a 3 Cycle Gaussian Pulse
(=0.6 au, TD-CIS)
6-31G(d,p) 6-31++G(d,p) 6-311++G(2df,2pd)
Current Research GroupDr. Peng Tao Dr. Barbara MunkJia Zhou Jason SonkBrian Psciuk Adam Birkholz
Recent Group MembersProf. Jason Sonnenberg, Stevenson University,Prof. Xiaosong Li, U. of WashingtonProf. Smriti Anand, Northern Virginia CollegeDr. Hrant Hratchian, Gaussian, Inc.Dr. Jie Li, U. California, Davis (Duan group)Dr. Stan Smith, Temple U. (Levis group)Dr. John Knox, GlaxoSmithKline (Singapore)Michael Cato, Jackson State U. (Leszczynski group)
Funding and Resources:National Science FoundationOffice of Naval ResearchNIHGaussian, Inc.Wayne State U.
AcknowledgementsCollaborators:
Dr. T. Vreven, Gaussian Inc.Dr. M. J. Frisch, Gaussian Inc.Prof. John SantaLucia, Jr., WSURaviprasad Aduri (SantaLucia group)Prof. G. Voth, U. of UtahProf. David Case, ScrippsProf. Bill Miller, UC BerkeleyProf. Thom Cheatham, U. of UtahProf. S.O. Mobashery, Notre Dame U.Prof. R.J. Levis, Temple U.Prof. C.H. Winter, WSUProf. C. Verani, WSUProf. E. M. Goldfield, WSUProf. D. B. Rorabacher, WSUProf. J. F. Endicott, WSU Prof. J. W. Montgomery, U. of MichiganProf. Sason Shaik, Hebrew UniversityProf. P.G. Wang, Ohio State U.Prof. Ted Goodson, U. of Michigan Prof. G. Scuseria, Rice Univ.Prof. Srini Iyengar, Indiana UProf. O. Farkas, ELTEProf. M. A. Robb, Imperial, London
Recent Group Members
Current Group Members